Signals may be modulated using phase-shift keying (PSK). In PSK modulation, changes in the phase of a signal are used to represent data. In multi-level PSK modulation, multiple bits may be transmitted per symbol, which allows for more data to be transmitted at a lower symbol rate. For example, 4-PSK modulation can transmit two bits per symbol, 8-PSK modulation can transmit three bits per symbol, and 16-PSK modulation can transmit four bits per symbol.
Multi-level PSK communication may impose particular requirements on a communication system. For example, multi-level PSK communication may be improved by communicating signals with purer phases. In general, a signal with a purer phase has shorter rise and fall times, and a signal with a pure phase may have essentially no rise or fall time. Known systems for modulating the signals, however, may not yield signals with satisfactorily pure phases.